HANNAN_RISSANEN

This function estimates autoregressive and moving-average parameters for a stationary time series using the Hannan-Rissanen multi-step approach.

The procedure fits a high-order autoregression to obtain residuals, then estimates ARMA coefficients using least squares, with an optional bias-correction stage when conditions are satisfied.

The function returns a row vector of estimated ARMA parameter values.

Excel Usage

=HANNAN_RISSANEN(endog, ar_order, ma_order, demean, initial_ar_order)

endog (list[list], required): Time-series observations as a 2D range (data points).
ar_order (int, optional, default: 0): Autoregressive order to estimate (lags).
ma_order (int, optional, default: 0): Moving-average order to estimate (lags).
demean (bool, optional, default: true): Whether to remove the mean before estimation (true/false).
initial_ar_order (int, optional, default: 0): Initial long autoregressive order used in first-stage residual estimation (lags).

Returns (list[list]): Row vector containing estimated ARMA parameter values.

Example 1: Hannan-Rissanen estimation for ARMA(1,1)

Inputs:

endog										ar_order	ma_order
5	5.2	5.1	5.4	5.3	5.6	5.5	5.8	5.7	6	1	1

Excel formula:

=HANNAN_RISSANEN({5,5.2,5.1,5.4,5.3,5.6,5.5,5.8,5.7,6}, 1, 1)

Expected output:

Result
0.466012	1.78856	0.0950253

Example 2: Hannan-Rissanen estimation for AR(2)

Inputs:

endog										ar_order	ma_order
12	12.5	12.1	12.8	12.4	13	12.7	13.3	13	13.6	2	0

Excel formula:

=HANNAN_RISSANEN({12,12.5,12.1,12.8,12.4,13,12.7,13.3,13,13.6}, 2, 0)

Expected output:

Result
0.0857862	0.855313	0.0929974

Example 3: Hannan-Rissanen estimation for MA(1)

Inputs:

endog										ar_order	ma_order
3	2.9	3.1	3	3.2	3.1	3.3	3.2	3.4	3.3	0	1

Excel formula:

=HANNAN_RISSANEN({3,2.9,3.1,3,3.2,3.1,3.3,3.2,3.4,3.3}, 0, 1)

Expected output:

Result
0.197778	0.0257315

Example 4: Hannan-Rissanen with explicit initial AR order

Inputs:

endog										ar_order	ma_order	initial_ar_order
8	8.3	8.1	8.5	8.2	8.6	8.4	8.8	8.6	9	1	1	4

Excel formula:

=HANNAN_RISSANEN({8,8.3,8.1,8.5,8.2,8.6,8.4,8.8,8.6,9}, 1, 1, 4)

Expected output:

Result
-2.2046	5.07056	0.0426358

Python Code

import numpy as np
from statsmodels.tsa.arima.model import hannan_rissanen as sm_hannan_rissanen

def hannan_rissanen(endog, ar_order=0, ma_order=0, demean=True, initial_ar_order=0):
    """
    Estimate ARMA parameters using the Hannan-Rissanen procedure.

    See: https://www.statsmodels.org/stable/generated/statsmodels.tsa.arima.model.hannan_rissanen.html

    This example function is provided as-is without any representation of accuracy.

    Args:
        endog (list[list]): Time-series observations as a 2D range (data points).
        ar_order (int, optional): Autoregressive order to estimate (lags). Default is 0.
        ma_order (int, optional): Moving-average order to estimate (lags). Default is 0.
        demean (bool, optional): Whether to remove the mean before estimation (true/false). Default is True.
        initial_ar_order (int, optional): Initial long autoregressive order used in first-stage residual estimation (lags). Default is 0.

    Returns:
        list[list]: Row vector containing estimated ARMA parameter values.
    """
    try:
        def to2d(x):
            return [[x]] if not isinstance(x, list) else x

        endog = to2d(endog)

        if not isinstance(endog, list) or not all(isinstance(row, list) for row in endog):
            return "Error: Invalid input - endog must be a 2D list"

        series = []
        for row in endog:
            for value in row:
                try:
                    series.append(float(value))
                except (TypeError, ValueError):
                    continue

        if len(series) < 6:
            return "Error: endog must contain at least 6 numeric values"

        init_order = None if int(initial_ar_order) <= 0 else int(initial_ar_order)

        params, _ = sm_hannan_rissanen(
            series,
            ar_order=int(ar_order),
            ma_order=int(ma_order),
            demean=bool(demean),
            initial_ar_order=init_order
        )

        if hasattr(params, "params"):
            values = np.asarray(params.params, dtype=float).ravel()
        elif hasattr(params, "to_array"):
            values = np.asarray(params.to_array(), dtype=float).ravel()
        else:
            values = np.asarray(params, dtype=float).ravel()

        return [values.tolist()]
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

endog *

Time-series observations as a 2D range (data points).

ar_order

Autoregressive order to estimate (lags).

ma_order

Moving-average order to estimate (lags).

demean

Whether to remove the mean before estimation (true/false).

initial_ar_order

Initial long autoregressive order used in first-stage residual estimation (lags).